M4E #102: Taguchi Quality Loss Function

In several ocassions we have covered the importance of quality in manufacturing. For example, in M4E #11 the concept of jidoka was explained. Today’s video from Quality Guru will explain the idea of Genichi Taguchi regarding quality and more specifically it will cover an overview of Taguchi Quality Loss function.

Time for Insights

• The underlying idea behind the Taguchi Quality Loss function is that any deviation (no matter how small) leads to a loss in quality, performance, or customer satisfaction. Mathematically, this loss is typically expressed through a quadratic function, such as the one below, where x is the observed value, T is the target value, and k is a constant that reflects the cost implications of deviation. This quadratic nature implies that the loss increases exponentially as the deviation grows larger, emphasizing the importance of precision in production and design.

  \(L(x) = k (x - T)^2\)

• The Taguchi method categorizes quality characteristics into different types such as nominal-the-best, smaller-the-better, and larger-the-better. This categorization helps in tailoring the loss function to the specific nature of the product or process being examined. For instance, while a slight deviation might be acceptable in one context, it might result in significant inefficiencies or increased wear in another.

• Imagine a manufacturing company that produces pistons for car engines. The ideal diameter of each piston is 50.00 mm, with an acceptable tolerance range of ±0.5 mm. Traditional quality control would consider any piston between 49.5 mm and 50.5 mm as acceptable and reject anything outside this range. However, the Taguchi Quality Loss Function suggests that even within this range, deviations from the target diameter result in performance losses, which can manifest as increased fuel consumption, engine inefficiency, or faster wear and tear.Using the Taguchi Quality Loss Function, the manufacturer can calculate the economic impact of these deviations. Suppose a deviation of 0.5 mm results in an additional $50 in maintenance costs over the engine’s lifetime. If the loss function is quadratic, a deviation of 0.25 mm would result in $12.5 of expected loss (50/4).